Is the curve single curvature or double (complex) curvature? Masking tape bends around curves pretty easily. And, if it is very narrow, it will conform even to double curvature. I would use a thin tape, like the Tamiya stuff.
The problem will be cutting narrow but uniform widths (I assume the space between the lines is narrow also). Cut with a stainless straight rule. The masking tape is reasonably cheap, so even if you have to discard the majority of the pieces you cut, you aren't wasting that much. Apply the tape to a piece of glass and then slice the narrow strips. 1/16 inch width is available at many hobby shops- you may not even have to slice that stuff.